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Programmability of Chemical Reaction Networks
"... Summary. Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a wellstirred solution according to standard c ..."
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Summary. Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a wellstirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and
Complexity, appeal and challenges of combinatorial games
 Proc. of Dagstuhl Seminar “Algorithmic Combinatorial Game Theory”, Theoret. Comp. Sci 313 (2004) 393–415, special issue on Algorithmic Combinatorial Game Theory
, 2004
"... Abstract Studying the precise nature of the complexity of games enables gamesters to attain a deeper understanding of the difficulties involved in certain new and old open game problems, which is a key to their solution. For algorithmicians, such studies provide new interesting algorithmic challenge ..."
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Abstract Studying the precise nature of the complexity of games enables gamesters to attain a deeper understanding of the difficulties involved in certain new and old open game problems, which is a key to their solution. For algorithmicians, such studies provide new interesting algorithmic challenges. Substantiations of these claims are illustrated on hand of many sample games, leading to a definition of the tractability, polynomiality and efficiency of subsets of games. In particular, there are tractable games that are not polynomial, polynomial games that are not efficient. We also define and explore the nature of the subclasses PlayGames and MathGames.
Scenic trails ascending from sealevel Nim to alpine chess
"... Abstract. Aim: To present a systematic development of part of the theory of combinatorial games from the ground up. Approach: Computational complexity. Combinatorial games are completely determined; the questions of interest are efficiencies of strategies. Methodology: Divide and conquer. Ascend fro ..."
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Cited by 17 (8 self)
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Abstract. Aim: To present a systematic development of part of the theory of combinatorial games from the ground up. Approach: Computational complexity. Combinatorial games are completely determined; the questions of interest are efficiencies of strategies. Methodology: Divide and conquer. Ascend from Nim to chess in small strides at a gradient that’s not too steep. Presentation: Informal; examples of games sampled from various strategic viewing points along scenic mountain trails illustrate the theory. 1.
Poset game periodicity
 INTEGERS Electr. J. Combin. Number Th
, 2003
"... Poset games are twoplayer impartial combinatorial games, with normal play convention. Starting with any poset, the players take turns picking an element of the poset, and removing that and all larger elements from the poset. Examples of poset games include Chomp, Nim, Hackendot, SubsetTakeaway, an ..."
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Poset games are twoplayer impartial combinatorial games, with normal play convention. Starting with any poset, the players take turns picking an element of the poset, and removing that and all larger elements from the poset. Examples of poset games include Chomp, Nim, Hackendot, SubsetTakeaway, and others. We prove a general theorem about poset games, which we call the Poset Game Perioidicity Theorem: as a poset expands along two chains, positions of the associated poset games with any ¯xed gvalue have a regular, periodic structure. We also prove several corollaries, including applications to Chomp, and results concerning the computational complexity of calculating gvalues in poset games.
Deciding the winner of an arbitrary finite poset game is pspacecomplete
 of Lecture Notes in Computer Science
, 2013
"... Abstract. A poset game is a twoplayer game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the poset loses. Polynomial time algorithms exist for ..."
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Abstract. A poset game is a twoplayer game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the poset loses. Polynomial time algorithms exist for certain restricted classes of poset games, such as the game of Nim. However, until recently the complexity of arbitrary finite poset games was only known to exist somewhere between NC1 and PSPACE. We resolve this discrepancy by showing that deciding the winner of an arbitrary finite poset game is PSPACEcomplete. To this end, we give an explicit reduction from Node Kayles, a PSPACEcomplete game in which players vie to chose an independent set in a graph. 1
Threerowed Chomp
 Adv. in Appl. Math
"... A “meta ” (pseudo) algorithm is described that, for any fixed k, finds a fast (O�log�a��) algorithm for playing 3rowed Chomp, starting with the first, second, and third rows of lengths a, b, and c, respectively, where c ≤ k, buta and b are arbitrary. © 2001 Academic Press How to Play CHOMP David G ..."
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A “meta ” (pseudo) algorithm is described that, for any fixed k, finds a fast (O�log�a��) algorithm for playing 3rowed Chomp, starting with the first, second, and third rows of lengths a, b, and c, respectively, where c ≤ k, buta and b are arbitrary. © 2001 Academic Press How to Play CHOMP David Gale’s famous game of Chomp [Ch] starts out with an M by N chocolate bar, in which the leftmosttopmost square is poisonous. Players take turns picking squares. In his or her (or its) turn, a player must pick one of the remaining squares, and eat it along with all the squares that are “to its right and below it. ” Using matrixnotation with the poisonous square being entry (1, 1), and the initial position consisting of the whole bar ��i � j��1 ≤ i ≤ M � 1 ≤ j ≤ N�, then picking the square �i0�j0 � means that one has to eat all the remaining squares �i � j � for which both i ≥ i0 and j ≥ j0 hold. The player that eats the poisonous (leftmosttopmost) square loses. Of course picking (1, 1) kills you, so a nonsuicidal player will not play that move unless forced to. For example, if M = 4 and N = 3, then the initial gameposition is
Grundy Sets of Partial Orders
"... Two players I and II are playing the Hackendot game, a slight variant of Hackenbush (see Berlekamp, Conway and Guy [1]) played on a partially ordered set P : First I chooses x 2 P and deletes the final section generated by x: he leaves the order P x , then II chooses y 2 P x and deletes the fin ..."
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Two players I and II are playing the Hackendot game, a slight variant of Hackenbush (see Berlekamp, Conway and Guy [1]) played on a partially ordered set P : First I chooses x 2 P and deletes the final section generated by x: he leaves the order P x , then II chooses y 2 P x and deletes the final section generated by y... and so on alternately. The player who cannot move loses the game. This kind of game was introduced by VonNeumann when the order P is a reverse ordered tree (the root is maximal). He concluded in this case that player I wins by a strategy stealing argument. In [5], ' Ulehla described how player I could win. We give an easy argument to calculate such a strategy for a wider class of partially ordered sets.
Recent results and questions in combinatorial game complexities
 NINTH AUSTRALASIAN WORKSHOP ON COMBINATORIAL ALGORITHMS
, 1998
"... Aim: Present a systematic development of part of the theory of combinatorial games from the ground up. Approach: Computational complexity. Combinatorial games are completely determined; the questions of interest are efficiencies of strategies. Methodology: Divide and conquer. Isolate the various di ..."
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Aim: Present a systematic development of part of the theory of combinatorial games from the ground up. Approach: Computational complexity. Combinatorial games are completely determined; the questions of interest are efficiencies of strategies. Methodology: Divide and conquer. Isolate the various difficulties separating hard from easy games, and attack them individually. Presentation: Informal; examples of games sampled from various levels illustrate the theory, with emphasis on formulating and motivating new and old research problems.
Flipping the winner of a poset game
 Information Processing Letters
, 2012
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On the Complexity of Computing Winning Strategies for Finite Poset Games
"... Abstract. This paper is concerned with the complexity of computing winning strategies for poset games. While it is reasonably clear that such strategies can be computed in PSPACE, we give a simple proof of this fact by a reduction to the game of geography. We also show how to formalize the reasoning ..."
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Abstract. This paper is concerned with the complexity of computing winning strategies for poset games. While it is reasonably clear that such strategies can be computed in PSPACE, we give a simple proof of this fact by a reduction to the game of geography. We also show how to formalize the reasoning about poset games in Skelley’s theory W 1 1 for PSPACE reasoning. We conclude that W 1 1 can use the “strategy stealing argument ” to prove that in poset games with a supremum the first player always has a winning strategy.